By assuming the underlying PDE terms are the same across multiple experiments, with potentially different coefficients, grouped sparsity allows to leverage the data across the experiments. The previous estimator can be generalised (inspired by [1]}) to grouped variables,
\(\hat{\tilde{\xi }}= \operatornamewithlimits{arg\,min}\Big ( \frac{1}{2n}||\partial _t u - \tilde{\Theta } \tilde{\xi }||_{F}^{2} + \lambda \sum _{g=1}^{p} \frac{||\tilde{\xi }_g||_{2}}{W_{g}} \Big )\) 
